Context: Gas ionized by starburst activity radiates radio recombination lines (RRLs), from which one can derive the plasma conditions and the number of massive stars formed in the burst, free of dust obscuration effects. Aims: We aimed to find detectable RRL emission from additional extragalactic starburst systems and to use the line properties to estimate the properties of the ionized gas. Methods: We conducted a search for RRLs in the nearby extragalactic starburst or Seyfert galaxies NGC 1808, the Circinus galaxy, NGC 4038/9, II Zw 40, NGC 6221, NGC 7552, IRAS 18325-5926, IC 5063, and VV 114. We used the Very Large Array with resolution of 3'' to 32'' and the Australia Telescope Compact Array with resolution of 10'' to search for the RRLs H91α and H92α with rest frequencies of 8.6 GHz and 8.3 GHz. From the new detections we derive conditions in the starburst regions. Results: We detected for the first time RRLs from the starburst nuclei in the Circinus galaxy and NGC 1808. The Circinus galaxy was detected in RRL emission with a line strength integrated over the source of 3.2 mJy, making it the fourth-strongest extragalactic RRL emitter known at this frequency (after NGC 4945, M 82, and NGC 253) and so is suitable for detailed study. The line and continuum emission from the Circinus galaxy can be matched by a model consisting of a collection of 50 to 10 000 H II regions with temperatures of 5000 K, densities of 500 cm-3 to 50 000 cm-3, and a total effective diameter of 3 pc to 50 pc. The Lyman continuum production rate required to maintain the ionization is 1 × 1052~s-1 to 3 × 1053~s-1, which requires 300 to 9000 O5 stars to be produced in the starburst, inferring a star formation rate of 0.2 M_ȯ yr-1 to 6 M_ȯ yr-1. NGC 1808 was detected in RRL emission at 3.9σ with a line strength of 0.47 mJy at the expected velocity. No radio recombination lines were detected from the other galaxies surveyed to a 3σ limit of 0.3 mJy to 1.4 mJy. Conclusions: We have detected RRLs from two galaxies, adding to the small but growing number of known extragalactic RRL emitters. The Circinus galaxy is strong and especially suited to high-quality follow-up spectroscopic study. We derived conditions and star formation rates in the starbursting regions. Uncertainties can be reduced by future multi-transition studies.
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